SIGNUM Manual
Contents
1. SIGNUM Simple Integrated Geomorphological NUmerical Model Version 1 0 User Manual A Refice refice ba issia cnr it Istituto di Studi sui Sistemi Intelligenti per l Automazione ISSIA Consiglio Nazionale delle Ricerche CNR Via Amendola 122 O 70126 Bari Italy January 2012 0020 Contents Contents 1 Introduction 2 Downloading and installing SIGNUM 3 Basic operations 4 Parameter file 4 1 GILmodulecalls oo 0c ee ees 42 Processing PALIO e iii ERR ADEE A A ees Li Surface setup AAA A ai aa GIL PASO escrita LTT 24 a 5 Process modules 5 1 SIGNUM diffusion linea ii be na AR ee panes 9 2 STGNUM Streampower esere ee Pa RI owe am 3 SIGNUM IPIETE Lila a Pen a 6 Developing new modules 6 1 The points structure e a 7 Output files 8 Ancillary and visualization functions 8 1 SIGNUM create Surface orean aa eed wee wo ew a a Des SIGNUM draw TIN o seneo sidi anya oR dna ORs Oe See Go SIGNUM cascade soe ad He eh eee hee be eG oe ee a a Oe SIGNUM PILOSA sso ua eee Cae See we a wae Go SIGNUM extract river gt o eed ee Bea eb eRe A da wee as 8 6 Callback_SelTINPointNumber 0 000000 pees References A GNU GENERAL PUBLIC LICENSE B Creative Commons license CONN NN O pa W wo 10 10 11 11 12 12 12 12 13 25 SIGNUM Manual 1 Introduction This document is a manual for the SIGNUM landscape evolution model The ac2. 766 28 yr dz_min 0 458 m dz_max 0 768 m SIGNUM elapsed time 2255 85 yr dt 628 79 yr dz_min 0 333 m dz_max 0 630 m SIGNUM elapsed time 3022 13 yr dt 766 28 yr dz_min 0 301 m dz_max 0 767 m SIGNUM elapsed time 116985 75 yr dt 396 47 yr dz_min 0 004 m dz_max 0 004 m SIGNUM elapsed time 117382 22 yr dt 396 47 yr dz_min 0 004 m dz_max 0 004 m SIGNUM elapsed time 117778 69 yr dt 396 47 yr dz_min 0 004 m dz_max 0 004 m SIGNUM elapsed time 118175 16 yr dt 396 47 yr dz_min 0 004 m dz_max 0 004 m apparent Steady State reached gt Figure 1 Typical output message sequence of the default SIGNUM operation SIGNUM run then a variable number of strings with information about the ongoing simulation such as the current simulated time the used time interval the minimum and maximum surface variations More information for each time step can optionally be printed out in verbose mode see sect 4 Such statements are printed for every simulation step until end of the simulation which will occur after a variable number of steps when either the total number of simulated years or an apparent steady state condition are reached The latter is given by the maximum absolute surface variation being below a predefined threshold see below for details A typical final surface evolved by using the default parameter file is shown on the front page of the present manual
3. SIGNUM Manual B Creative Commons license This Manual is licensed under the Creative Commons Attribution NonCommercial ShareAlike 3 0 Unported License To view a copy of this license visit http creativecommons org licenses by nc sa 3 0 or send a letter to Creative Commons 444 Castro Street Suite 900 Mountain View California 94041 USA 25
4. This particular example represents a surface of size 1000 m x 1000 m sampled randomly but uniformly with maximum point spacing of 50 m evolved until steady state under a combination of diffusion channeling and uplift processes Note that the vertical scale is exaggerated of a factor of 100 with respect to the horizontal dimensions 4 Parameter file SIGNUM is designed to be controlled entirely through a parameter file which consists of a standard Matlab m file script containing a series of variable definitions Note that any custom parameter file will be executed after definition of the default values for all input variables in the main program so any variable not defined in the parameter file is assumed to be set at its default value To avoid missing overriding statements the user is advised to use a parameter file template such as the one listed in fig 2 which can be modified and customized at will The main parts of the template parameter file are described in the following 4 1 GTL module calls The first three statements define the process modules The process module calls DIFFUSION_MODULE_CALL CHANNELING_MODULE_CALL and UPLIFT_MODULE_CALL are strings containing standard Matlab calls to functions implementing the three basic types of ge omorphic transport laws GTL The process modules are defined in detail in sect 5 SIGNUM Manual 4 1 GTL module calls Call function SIGNUM SIGNUM_parameter_file_templ
5. 3 Ke m and n are model parameters specified in the parameter file see fig 2 The correct syntax to be used in the assignment of the CHANNELING_MODULE_CALL string in this case is as shown dz dtnew SIGNUM streampower kc mc nc dt The dt input variable represents the current value of the time step interval the outputs are the array dz of the height changes due to the channeling GTL in this case the stream power law and the time step dtnew to be used in the next time step The latter is calculated within the function as a function of the surface states and parameters in order to satisfy the Courant condition see 3 for details In the present version any of the kc mc and nc parameters can be defined as spatial variables in the sense that they can be vectors of the same length as the points structure with one value for each surface point In this way spatially variable stream power erosion conditions can be simulated K A Vz 3 5 3 SIGNUM uplift This function calculates height variations due to a global rule i e a spatial field of constant uplift of all the points representing the surface oz Cami 5 where uf is a parameter to be assigned in the parameter file The correct syntax to be used in the assignment of the UPLIFT_MODULE_CALL string in this case is as shown dz SIGNUM uplift uf dt 1 The dt input variable represents the current value of the time step interval the outputs are th
6. The next part contains the check for any existing surface file First existing SIGNUM output files with assigned time evolution number are checked for existence The string Start_time is used to this end In the listing in fig 2 this statement is commented Suppose you have a SIGNUM run which has been run until a simulated time of say 300 ky Suppose the exact integer number of simulated years is 300037 as in the example You want to evolve this surface for some further simulated time You should then look for a SIGNUM output file with the form lt Run_name gt __Time_300037 mat In this case assign the correct lt Run_name gt variable then the correct Start_time value SIGNUM will then load the existing mat file and start to evolve the surface from the existing configuration with the parameters specified in the subsequent parts of the parameter file thresh river This is the threshold to be used in the figure plot to highlight rivers with blue lines Mesh node links in the TIN originating from points with contributing areas greater than this threshold are plotted as rivers i e as blue lines with thickness proportional to the contributing area If this variable is set to zero an automatic threshold is used by the plotting function plot_surface The time frequency of update for the graphical representation of the simulated surface Setting this to zero disables surface plotting output mat file Name kernel string for the output
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8. by summing contributions over all j 1 n prime neighbors of point i The kz parameter should be assigned in the parameter file see the corresponding section and the kd assignment in the template parameter file in fig 2 The correct syntax to be used in the assignment of the DIFFUSION_MODULE_CALL string inthis case is as shown dz dtnew SIGNUM_diffusion_linear kd dt The dt input variable represents the current value of the time step interval the outputs are the array dz of the height changes due to the diffusion GTL and the time step dtnew to be used in the next time step The latter is calculated within the function as a function 5 Process modules of the surface states and parameters in order to satisfy the Courant condition see 3 for details In the present version the kd parameter can be defined as a spatial variable in the sense that it can be a vector of the same length as the points structure with one value for each surface point In this way spatially variable diffusion constants can be simulated 5 2 SIGNUM_streampower This function calculates height variations according to the formula oz ot see eq 9 and references in 3 for justification and details Here again the surface slope is approximated over the edges of the Delaunay TIN mesh and the contributing area A is calculated over the Voronoi polygons as n dz z Chi KA 4 ot C i Lij see eq 10 in
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10. mat files In the example the variable is set equal to the Run_name string to have consistent file names log_file name If set to a nonempty string a log file name is generated through Mat lab s journal function containing transcription of all the command window contents in the session N save Frequency at which output mat files are saved Note that due to the Courant limit the actual value of the simulated times at which output file save will occur will fluctuate For instance is N_save is set to 1000 years output files will have names such as 1003 2028 etc N_epochs The number of years the simulation is scheduled to last The simulation will go on until N_epochs years have been simulated unless steady state is reached earlier verbose Flag to output more information strings on screen during execution The messages are also recorded in the log file if the log_file_name variable is set dzSS This is the maximum absolute surface height variation Whenever maximum absolute surface height variation between two successive iterations falls below this value the simulation is stopped and a message issued that an apparent steady state has been reached SIGNUM Manual 4 3 Surface setup 4 3 Surface setup In this section the initial model surface is set up In the template example an ancillary function SIGNUM_create_surface is used see sect 8 1 for further details This can be substituted by other procedures for
11. modes of generation of the surface points can be used one which makes use of the Matlab Partial Differential Equation PDE Toolbox function initmesh which generates a mesh of points inside closed regions of any shape see Matlab PDE Toolbox documentation for further details and another which only uses default functions and 10 SIGNUM Manual 8 2 SIGNUM draw_TIN creates the points by perturbing a regular rectangular array of points by random quan tities The choice of the generation mode is controlled by the code flag Additional inputs control the size of the surface and the maximum or mean spacing of points An initial uniform tilt can be assigned to the surface in the x direction through the z_slope parameter or a wedge shape if z_slope is a 2 valued array A gaussian distributed noise can be added to the surface elevation with st dev controlled by the z_noise parameter Finally a bcode flag controls the state of the four boundary sides of the surface which affect the subsequent simulation open boundaries are usually kept to low height values e g zero so that sediment and water are allowed to flow through them and out of the surface closed boundaries are treated as delimiting periodic boundary conditions so material and or water flow is forbidden through them Four configurations are foreseen for the sides of the rectangular surface namely generating either all 4 sides open bcode 0 left and right sides open and the
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17. _river 5e4 threshold contrib area for plotting blue rivers plot_surface 1000 plot surface every years output_mat_file Run_name logfilename Run_name log N_save 10000 save surface every years N_epochs 1000000 number of simulation years verbose Q dzSS 0 00001 m year lt Threshold max height change for steady state A Surface setup x y z b SIGNUM_create_surface 2 1 perturbed grid else uses PDE 0 1000 0 1000 coordlins 50 points spacing 0 01 perturb_xy not valid for PDE method 0 z_slope 1 0 z_noise 0 bcode all 4 boundaries open 1 left and right x 0 x max boundaries open the rest closed 2 upper and lower y 0 y max boundaries open the rest closed 3 all 4 boundaries closed except 0 0 corner which is open A ee nnn ncn cen GTL parameters Linear diffusion parameters kd le 2 linear diffusivity constant m 2 year Channeling parameters kc 1e 4 mc 0 5 nc 1 Uplift parameters uf le 3 constant uplift rate m year Figure 2 SIGNUM parameter file template 4 Parameter file 4 2 Processing parameters In this section some miscellaneous parameters and states are defined Run_name This string is used as an identification at the beginning of the names of the output files generated by the model Start_time and check for previous data
18. ate Copyright C 2011 2012 the authors This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the License or at your option any later version This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details A GTL Module calls Call lines for the GTL modules to be used by the model Output names and dt final input name are mandatory Do not forget the final semicolon within the quotes to avoid spurious screen output DIFFUSION_MODULE_CALL dz dtnew SIGNUM_diffusion_linear kd dt CHANNELING_MODULE_CALL dz dtnew SIGNUM_streampower kc mc nc dt UPLIFT_MODULE_CALL dz SIGNUM_uplift uf dt Processing parameters Run_name SIGNUM_test Start_time 300037 lt uncomment to start from an existing surface if exist Start_time var load Run_name __Time_ num2str Start_time mat elseif exist Run_name _initial_surface mat file disp Found file Run_name _initial_surface mat loading load Run_name _initial_surface mat end thresh
19. buting area of each point scalar indices of upslope contributing points 1 D array of variable size flux from contributing points 1 D array of variable size height of following point scalar index of following point scalar indices of preceding points 1 D array of variable size border flag 0 1 or 2 scalar of a predefined string which is set in the parameter file default is SIGNUM_output then the __Time_ string note the double underscore and a final part consisting of the current evolution simulated time rounded to the nearest integer An initial mat file is also generated with the time string substituted by the string initial_surface containing the initial surface states unless the model is run by load ing an existing surface e g if the Start_time is set in the parameter file see sect 4 If the logfilename variable is set also a text log file is output containing all the screen output by the program 8 Ancillary and visualization functions Some ancillary functions are present in the SIGNUM distribution to help create and manage simulated TIN surfaces They are described in the following 8 1 SIGNUM_create_surface This function creates three vector arrays representing the x y z coordinates of a syn thetic surface as well as a boundary flag vector The points coordinates are sampled uniformly to form a TIN surface of rectangular shape with user controlled characteris tics Two
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22. cture is built by a specific m function called SIGNUM init points This function can be inspected and edited customised at will to add further fields Note that mesh edges as well as all edge related quantities such as slopes etc are stored point wise thus doubling the space requirements Future releases will probably address this issue 7 Output files The main output of the model is a series of mat files each containing the entire Matlab memory content at a particular simulated time step The files have names consisting 8 Ancillary and visualization functions Table 1 Field names of the points structure The comments describe the entry and its size For instance the field points i slopes is an array containing the values of the slopes of all the Delaunay edges connected to point i after 3 Field name Comment x y z coordinates scalars adjacents indices of all adjacent points 1 D array of variable size n slopes slope value for every edge delaunay_edges voronoi_edges voronoi_area voronoi_coordinates contrib_area contrib_points contrib_flux z_following following preceding border 1 D array of variable size n lengths of planar Delaunay edges connected to each point 1 D array of variable size n lengths of Voronoi edges of each voronoi polygon 1 D array of variable size n area of Voronoi polygon scalar coordinates of Voronoi vertices 1 D array of variable size n contri
23. e array dz of the height changes due to the uplift GTL in this case constant uplift In the present software version the uf The Courant Friedrichs Lewy CFL condition or Courant condition for short is an upper limit condition on the simulation time step which applies in general to the solution of partial differential equation problems through explicit finite elements methods SIGNUM Manual parameter can be defined as a spatial variable in the sense that it can be a vector of the same length as the points structure with one value for each surface point In this way spatially variable uplift patterns can be simulated 6 Developing new modules The SIGNUM model is designed to be easy to understand tweak and customize As in this initial version only basic modules and processes are implemented we strongly encourage hacking and adaptation of process functions implementation of innovative GTLs and algorithms as well as any other improvement from the scientific community To develop new GTL modules first write a new m Matlab function implementing the GTL as a function of the states stored in the points global structure see below as well as any necessary parameter To perform this step make sure that the calling syntax for the new GTL function is consistent with the default GTL functions described above in particular that one of the input is the current time step dt and one of the outputs is the GTL contribution to the
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28. he SIGNUM model with the default parameters which generate a sample surface of size 1000 m x 1000 m subject to uniform uplift uniform linear diffusion and uniform stream power erosion with nominal parameters These values are used only as a representative test case Normal operation will almost invariably require setting up parameters in a custom parameter file to be passed to the program To use custom parameters it is possible to specify an alternative parameter file name which must be an m file in the current path or in the Matlab path So for instance a command such as SIGNUM myparameters can be entered at the command prompt which says to SIGNUM to use the file myparameters m as parameter file Once started the program starts producing output which consists of e aseries of strings on the Matlab command window e a series of mat files in the current directory e optionally a figure window showing the evolving surface updated periodically A typical series of output messages obtained by running the default parameters is shown in fig 1 It consists of a string summarizing information about the current 4 Parameter file gt gt SIGNUM No parameter file selected ds SIGNUM starting with default parameters Starting main cycle on 1000000 years SIGNUM elapsed time 0 00 years SIGNUM elapsed time 860 78 yr dt 860 78 yr dz_min 0 829 m dz_max 0 863 m SIGNUM elapsed time 1627 06 yr dt
29. height variation dz If transient effects are implemented such as in the default cases of diffusion and channeling erosion another output should be the new maximum time step allowed by the Courant condition dtnew Then substitute the new function call in your custom parameter file e g modifying one of the three module calls and add modify all the necessary parameters in the corresponding section of the same file If the new function needs to define new fields in the points structure these can be easily added or modified by editing the SIGNUM init points function Many other improvements can be conceived based on this skeletal recipe so feel free to experiment We d be happy to receive notice of any use of the model so feel free to contact the author via e mail 6 1 The points structure The points structure is the basic array containing all the states of the simulated surface at any time step It is defined as a global variable so that it is not necessary to pass it as an argument to the various sub functions This solution is often used in Matlab as a valid substitute for the standard pass by reference procedure available in other languages to avoid unnecessary memory storage The points structure consists of a series of records one for every surface point with fields containing information related to that point The fields present in the structure in this software version are reported in tab 1 reproduced from 3 The points stru
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31. iments Geografia Fisica e Dinamica Quaternaria 34 75 80 2011 3 A Refice E Giachetta and D Capolongo SIGNUM a Matlab TIN based Land scape Evolution Model Computers amp Geosciences 2012 In press 12 SIGNUM Manual A GNU GENERAL PUBLIC LICENSE Version 3 29 June 2007 Copyright 2007 Free Software Foundation Inc http fsf org Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed The GNU General Public License is a free copyleft license for software and other kinds of works The licenses for most software and other practical works are designed to take away your freedom to share and change the works By contrast the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program to make sure it remains free software for all its users We the Free Software Foundation use the GNU General Public License for most of our software it applies also to any other work released this way by its authors You can apply it to your programs too When we speak of free software we are referring to freedom not price Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software and charge for them if you wish that you receive source code or can get it if you want it that you can change the software or use pieces of it in new free programs and that you
32. ing organizations If propagation of a covered work results from an entity transaction each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party s predecessor in interest had or could give under the previous paragraph plus a right to possession of the Corresponding Source of the work from the predecessor in interest if the predecessor has it or can get it with reasonable efforts You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License For example you may not impose a license fee royalty or other charge for exercise of rights granted under this License and you may not initiate litigation including a cross claim or counterclaim in a lawsuit alleging that any patent claim is infringed by making using selling offering for sale or importing the Program or any portion of it Patents A contributor is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based The work thus licensed is called the contributor s contributor version 20 SIGNUM Manual A contributor s essential patent claims are all patent claims owned or controlled by the contributor whether already acquired or hereafter acquired that would be infringed by some manner permitted by this License of making using or selling its contributor version but do not include claims t
33. llowing attribute Point indices can be evidenced on a Matlab figure showing the TIN structure by using the callback function described in the next section 8 6 Callback SelTINPointNumber This is a callback function which can be used as a substitute for the standard one in the Matlab function showing the current SIGNUM mesh surface to highlight a particular point index in the points structure This is useful to identify a particular point on the surface e g with the purpose of extracting all points downslope through the SIGNUM extract_river function described above in sect 8 5 To use it make sure you have created a Matlab figure showing a SIGNUM sur face as a TIN structure e g through use of the above described SIGNUM draw_TIN function see sect 8 2 Then click on the toolbar button Data cursor In the context menu click on Select Text Update Function then browse and select the Callback_SelTINPointNumber m function within the standard open file dialogue and click OK Now clicking on a point on the TIN surface you should see a pop up window containing as additional information the current point index indicated as Pid References 1 J Braun and M Sambridge Modelling landscape evolution on geological time scales a new method based on irregular spatial discretization Basin Research 9 27 52 1997 2 D Capolongo E Giachetta and A Refice Numerical framework for geomorpho logical exper
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39. rest closed bcode 1 upper and lower sides open and the rest closed bcode 2 or all sides closed except for the single point in the origin x y 0 which is kept open and serves as single surface outlet bcode 3 The SIGNUM_create_surface is used typically within the parameter file to easily generate synthetic surfaces of various kinds Note that in this software version only the point coordinates and boundary codes have to be created within the parameter file and passed to the main program The TIN structure Delaunay triangulation and Voronoi polygon structure is built within the SIGNUM program through the SIGNUM_assign structure sub function which is essentially a wrapper to the Matlab delaunay triangulation function 8 2 SIGNUM draw TIN This function draws any TIN simulated through SIGNUM as a 3 D surface using a topographic colormap and optionally highlights rivers as TIN edges connecting points with cumulated drainage area above a given threshold The function accepts as input the SIGNUM points structure as defined in the main program see sect 6 1 as well as an optional threshold for river plotting The twin function SIGNUM_draw_TIN_g requires the presence of the global points structure in memory Typical usage is by first loading one of the output mat files relative to a given simulated time step then launching the function with only one optional argument the threshold area 8 3 SIGNUM cascade Thi
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41. ronym SIGNUM stands for Simple Integrated Geomorphological NUmerical Model and is a TIN based landscape evolution model written in Matlab code The software is distributed under the GNU GPL license version 3 see appendix A Its documentation this manual is distributed under the Creative Commons license see appendix B A thorough description of the software operation as well as its scientific basis and some example applications can be found in publications such as 3 or 2 2 Downloading and installing SIGNUM The SIGNUM code can be downloaded from the Surface Processes and Quantitative Geomorphology Group website Please always refer to the above site for latest software updates We d be also glad to receive news about bugs and possibly fixes modifications and any other use of the software The package comes in a zip file containing all the necessary m files to run the code For best results unpack unzip the file in a separate directory then add the directory to your Matlab path see the Matlab documentation for how to do this In this way you will be able to access the SIGNUM program files while working in any other directory which is useful to handle various simulations and projects with possibly different parameters and processes 3 Basic operations If the SIGNUM installation directory is in your Matlab path running SIGNUM is as simple as starting Matlab and typing SIGNUM at the Matlab command prompt This starts t
42. s function implements the cascade algorithm described in 1 it is used within the SIGNUM model to derive a correct visiting order of the TIN nodes to calculate the contributing areas It has an optional second output which is an index array containing integer flags for detected hydrological basins all points belonging to the same basin will share the same index in the ncat output array This is useful to perform hydrologic geomorphologic analyses on the simulated surfaces The function accepts as input the SIGNUM points structure as defined in the main program see sect 6 1 The twin function SIGNUM_cascade_g requires the presence of 11 References the global points structure in memory 8 4 SIGNUM plot_SA This function plots the slope vs area log log chart of all the points contained in a SIGNUM points structure The twin function SIGNUM_plot_SA_g requires the presence of the global points structure in memory 8 5 SIGNUM extract_river This function extracts the sequence of surface points from a given one which is passed to the function as input to a final point which usually coincides with a surface outlet The function requires the presence of the global points structure in memory The input is an index pointing to one record of the points structure The output is the sequence of indices of points hydrologically linked on the surface starting from the input point i e all the points subsequently linked by the fo
43. setting up triangulated surface e g by loading external DEM data 4 4 GTL parameters This section of the parameter file contains the relevant parameters for the three GTL functions listed at the beginning All the input parameters for each GTL function must be defined here except for the dt variable 5 Process modules Surface height changes at each iteration are computed by applying a series of geo morphic transport laws GTL which are coded as Matlab functions acting on the global points structure as described below Three basic types of GTL are foreseen in the present version of the code namely diffusion channeling and uplift These are assigned through the DIFFUSION_MODULE_CALL the CHANNELING_MODULE_CALL and the UPLIFT_MODULE_CALL strings assigned in the parameter file as shown in sect 4 The default functions for each of these three process types are described in the following 5 1 SIGNUM diffusion linear This function calculates height variations according to the formula Z un cri kgV z 1 see eq 3 in 3 Surface curvature V2z is approximated through computation of the surface slopes on the arcs L of the usually Delaunay triangulation composing the TIN the Voronoi polygon side lengths A and the point contributing area Aj as oz kav Zi Zi rei ara 2 i j l ij see eq 4 and references in 3 for justification and details Here the contribution to height variation of the point iis calculated
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